South Africa's deputy president has promised to conclude a power transition in which he would succeed Jacob Zuma, who faces widespread calls to resign because of corruption allegations.

Standing on the balcony of Cape Town's pillared City Hall, Deputy President Cyril Ramaphosa consolidated his control of the government on Sunday.

He delivered what amounted to a state of the nation address of the kind that President Zuma was unable to give as scheduled last week because of the leadership crisis in South Africa.

Mr Ramaphosa, Mr Zuma's expected successor, set out a policy agenda for the year in his nationally televised speech, which marked the start of commemorations of the centenary of Nelson Mandela's birth on July 18 1918.

Then he referred to the topic that people really wanted to hear about - his confidential negotiations in recent days with Mr Zuma over the president's exit after a scandal-marred tenure.

The ruling ANC party's national executive committee will discuss Mr Zuma's fate at a meeting on Monday "and because our people want this matter to be finalised, the national executive committee will be doing precisely that," Mr Ramaphosa said.

He said his discussions with Mr Zuma had to be conducted with "care and purpose" and with the aim of uniting South Africans.

The political opposition criticised the private talks, saying the 75-year-old president may have been pressing for an "exit package" in exchange for his resignation.

The Democratic Alliance, the biggest opposition party, referred to unconfirmed media reports that Mr Zuma demanded a state security detail for himself and his family as well as payment by the state of his legal fees.

"He must be prosecuted and, if found guilty, be locked up for his crimes," the Democratic Alliance said.

Mr Zuma denies wrongdoing, but he has been discredited by scandals, including multi-million-dollar upgrades to his private home that were paid by the state.

There has also been alleged looting of state enterprises by his associates and the possible reinstatement of corruption charges tied to an arms deal two decades ago.

In his speech, the deputy president said the government will wage a "relentless war against corruption and mismanagement of the resources of our country" and that the justice system will punish the guilty.

Mr Ramaphosa, 65, joined Mr Zuma's cabinet as deputy in 2014 and replaced the president as head of the African National Congress in December.

He has faced criticism for previously keeping a low profile on the issue of corruption for much of his time as Mr Zuma's deputy, though supporters say he was biding his time and planned to engineer changes from within the government and ruling party.